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During the dinner hour, the distribution of the inter-arrival time of customers at a restaurant is estimated to be as shown below. The mode of payment and the service times of the cash and credit card customers are shown in the following tables. Complete the tables and simulate the system for 20 customer arrivals and determine the average time a cash and credit card customer must wait in line before paying the cashier. Use Column A of the given random number table to determine the customer inter-arrival time, Column B to determine whether the customer pays with cash or credit, and Column C to determine the service time. Inter-arrival time Inter-arrival Time Probability Cumulative Probability Random Number Interval 30 seconds 0.45 60 seconds 0.25 90 seconds 0.15 120 seconds 0.10 150 seconds 0.05 Mode of Payment Payment Mode Probability Cumulative Probability Random Number Interval Cash 0.6 Credit Card 0.4 Cash Service Time Service Time Probability Cumulative Probability Random Number Interval 20 seconds 0.35 40 seconds 0.30 60 seconds 0.25 80 seconds 0.10 Credit Card Service Time Service Time Probability Cumulative Probability Random Number Interval 30 seconds 0.20 60 seconds 0.45 90 seconds 0.25 120 seconds 0.10 Random Numbers (A) (B) (C) 6320 1094 1995 4630 7371 7971 8657 2809 3554 0030 5148 6300 5624 9115 5495 6728 1469 5165 5925 6480 9339 2829 2447 6997 7939 7031 1443 6476 8442 3574 3319 7387 0150 8134 1788 0933 1712 4891 7082 6317 1149 5025 6605 8822 4081 2734 9451 4100 0432 2990 7190 3441 8314 6822 0726 7176 5053 6969 2766 8284 Complete the table below to show the results of the simulation. Customer Random Number Arrival Time Random Number Mode of Payment Random Number Service Time Service Time Waiting Time Begins Ends Cash Credit 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Average Waiting Time (Cash)= Average Waiting Time (Credit)= Please do in word, not excel. Please see attached word file for formatting
QSO510 Evaluate 10.1.doc

QSO 510: Module 10
Notes: Before doing this assignment, do the practice problem posted under Apply and Discover. Wordprocess your answers within this document. Do not create a new file. Show all steps used in arriving at
the final answers. Incomplete solutions will receive partial credit.
Problem
During the dinner hour, the distribution of the inter-arrival time of customers at a restaurant is estimated
to be as shown below. The mode of payment and the service times of the cash and credit card
customers are shown in the following tables. Complete the tables and simulate the system for 20
customer arrivals and determine the average time a cash and credit card customer must wait in line
before paying the cashier. Use Column A of the given random number table to determine the customer
inter-arrival time, Column B to determine whether the customer pays with cash or credit, and Column C
to determine the service time.
Inter-arrival time
Inter-arrival Time

Probability

30 seconds
60 seconds

0.15

120 seconds

0.10

150 seconds

Random Number
Interval

0.45

90 seconds

Cumulative
Probability

0.05

0.25

Mode of Payment
Payment
Mode

Probability

Cash

0.6

Credit Card

Cumulative
Probability

Random Number
Interval

0.4
Cash Service Time

Service Time

Probability

20 seconds
40 seconds

0.35
0.30

60 seconds

0.25

80 seconds

0.10

Cumulative
Probability

Random Number
Interval

Credit Card Service Time
Service Time

Probability

30 seconds
60 seconds

0.20

90 seconds

0.25

120 seconds

0.10

Random Numbers
(A)

(B)

(C)

6320

1094

1995

4630

7371

7971

8657

2809

3554

0030

5148

6300

5624

9115

5495

6728

1469

5165

5925

6480

9339

2829

2447

6997

7939

7031

1443

6476

8442

3574

3319

7387

0150

8134

1788

0933

1712

4891

7082

6317

1149

5025

6605

8822

4081

2734

9451

4100

0432

2990

7190

3441

8314

6822

0726

7176

5053

6969

2766

8284

0.45

Cumulative
Probability

Random Number
Interval

Complete the table below to show the results of the simulation.

Custome
r

Rando
m
Numbe
r

Arriva
l
Time

Rando
m
Number

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Average Waiting Time (Cash)=
Average Waiting Time (Credit)=

Mode of
Payment

Rando
m
Numbe
r

Servic
e
Time

Service Time
Begin End
s
s

Waiting Time
Cash

Credit

4

QSO 510: Module 10

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